Fully Orthogonal Multi-Carrier Predistortion Linearization for RF Power Ampliﬁers

Xi Yang 1, Patrick Roblin 1, Dominique Chaillot 2, Shashank Mutha 1, Jeff Strahler 3, Jiwoo Kim 1, Mohammed Ismail 1, John Wood 4, John Volakis 1

1 Electrical and Computer Engineering, The Ohio State University, Columbus, OH 43210, USA 2 CEA/CESTA, 33114 LE BARP, France 3 Andrew Corporation, Westerville, OH 43082, USA 4 Freescale Semiconductor, Inc., RF Division, 2100 E. Elliot Road, Tempe, AZ 85284, USA

Abstract— This paper presents a fully orthogonal frequency- this orthogonality condition since the interband predistortion selective baseband predistortion linearization system for RF generated undesirable inband frequency components. Thus multi-carrier power amplifiers (PA) affected by strong differential multiple iterative linearization steps between the inband and memory effects. A new scheme is introduced for removing the unwanted inband frequency components generated by the interband linearization had to be carried out to achieve opti- interband predistortion corrections, thus establishing full orthog- mal linearization result. This non-orthogonal implementation onality between the interband and inband predistortion. The which unnecessarily correlates interband and inband makes demonstration study is performed on a two-carrier OFDM signal any subsequent auto-adaptive linearization more difficult and of 8 MHz bandwidth each, separated by 16 MHz for a total requires more demodulation bandwidth (higher cost). So in RF bandwidth of 32 MHz. Both the OFDM signal generator and the new orthogonal multi-carrier linearization algorithm this work we propose and demonstrate an improved im- proposed were implemented in a field programmable gate array plementation of the frequency-selective algorithm baseband (FPGA) and applied to the experimental investigation of the predistortion with full orthogonality. linearization of a Class AB/Class C LDMOS PA at 3.5 GHz. It is This paper follows the following organization. In Section demonstrated that with the new orthogonality implementation, 5 II (theory) we will (1) introduce the embedded OFDM signal dB inband distortion introduced by the interband predistortion steps is automatically suppressed such that multiple iterative generator used for this work and (2) present the algorithm used steps between the interband and inband linearizations are no for orthogonality implementation. In Section III and IV, the longer required in the optimization. Adjacent channel leakage FPGA implementation of the algorithm and the experimental ratio (ACLR) of up to -45 dBc for inband and interband are linearization results will be presented. In the conclusion we demonstrated experimentally. will summarize the results obtained and benchmark them. Index Terms— Linearization, memory effect, orthogonality, power amplifiers, predistortion. II. BASEBAND PREDISTORTION LINEARIZATION WITH FULL ORTHOGONALITY IMPLEMENTATION I. INTRODUCTION In the previous work [3], due to the multiplication of the in- 2 The development of auto-adaptive linearization algorithm terband envelop Einter with the inband I and Q, two undesired [1] [2] has become more and more important for wireless inband components were generated besides the desired inter- basestation RF multi-carrier power amplifiers (PAs) and is band terms. This effect is referred in this paper as the interband expected to play a key role in software defined radio (SDR) predistortion not being orthogonal to the inband predistortion. applications. As shown in Fig.1, the interferences generated from interband Recently an algorithm for baseband vector predistortion predistortion increase the inband spectrum regrowth, degrading linearization capable of frequency-selectively reducing the the inband linearization previously achieved. Note that for inband and interband spectrum regrowth for RF multi-carrier best performance it was demonstrated in [3] that the inband power amplifiers (PAs) affected by strong differential memory linearization must be performed before interband linearization. effects was reported [3]. One of the advantages for the So in this work, we propose an additional block extending the frequency selective approach is that the auto-adaptive lin- previous work, to realize a fully orthogonal implementation. earization can be carried out separately for each band, greatly reducing the channel bandwidth needed by the receiver used A. OFDM Signal Generator in the adaptation. This requires that inband and interband In this work, 64 tones OFDM signal generators were predistortions are fully orthogonal. However, the original implemented in the FPGA test-bed. Each generator provides frequency selective implementation [3] did not fully satisfy uncorrelated quadrature I and Q signals, which can be BPSK

978-1-4244-2804-5/09/$25.00 © 2009 IEEE 1077 IMS 2009 is used to generate exact Hilbert signal pairs IL(t) (−QL(t)) −55 Interband predistortion I (t) Q (t) I I Interferences and U ( U ) for the 64 OFDM L and U signals for Interband predistortion −60 with ortho the required LSB and USB ﬁltering.

−65 The principle of the orthogonality implementation is the following: with proper processing of the outputs of the inband −70 linearization stage, two inband frequency components will be Spectrum (dBm) −75 generated and added to the interband predistortion outputs to −80 cancel the interferences the latter one generates. The system 3.45 3.46 3.47 3.48 3.49 3.5 3.51 3.52 3.53 3.54 3.55 (a): Without fundamental bands diagram is shown in Fig.3, where the inband and interband predistortion parts remain the same as in [3]. Here, we intro- −40 Interband predistortion duce a new orthogonality implementation block to make the Interband predistortion −50 with ortho interband predistortion orthogonal to the inband predistortion. Interferences Since the interband predistortion is positioned after the inband −60 2 predistortion, the inband envelop Einband is calculated by using the IU , IL, QU and QL:

Spectrum (dBm) −70 2 2 2 Einband(t)=EU (t)+EL (t) −80 2 3.45 3.46 3.47 3.48 3.49 3.5 3.51 3.52 3.53 3.54 3.55 2 2 (b): With fundamental bands EU (t)=IU (t)+I (t) Frequency (GHz) U 2 2 2 EL (t)=IL (t)+IL(t)

Fig. 1. Interband predistortion impacts on inband for non-ortho and Two new coefﬁcients IMDLcorr and IMDUcorr, which orthogonal implementation without (a) and with (b) the two carriers are calculated from the interband predistortion parameters α3 (up-converted signals without passing through PAs). and β3 are introduced: α∗ + jβ∗ CCDF for OFDM Signals (16 MHz) 3 3 2 IMDLcorr = 10 1+j α3 + jβ3 IMDUcorr = 1 10 1+j The coefﬁcients for the digital modulator are then given by:

0 10 2 αLortho(t)=−Re [IMDLcorr] EU (t) 2 βLortho(t)=−Im [IMDLcorr] EU (t) −1 10 2 αUortho(t)=−Re [IMDUcorr] EL (t) 2 βUortho(t)=−Im [IMDUcorr] EL (t) −2 10 The resulting ILortho, QLortho, IUortho and QUortho after

Percentage of the signal above power specified by x−axis [%] the digital IQ modulator are: −3 10 0 1 2 3 4 5 6 7 8 9 PAPR [dB] ILortho = αLorthoIL − βLorthoQL QLortho = βLorthoIL + αLorthoQL = −I Lortho Fig. 2. CCDF plot of OFDM PAPR IUortho = αUorthoIU − βUorthoQU QUortho = βUorthoIU + αUorthoQU = I Uortho or QPSK modulated with adjustable symbol duration. In The output of the orthogonality block is then obtained by order to approximate a typical OFDM communication PAPR, reconstituting Iortho and Qortho: several techniques were used: (1) each tone starts with equally Iortho = IUortho + ILortho distributed phases for the unmodulated case and (2) uses a Q = Q + Q 17-bit Galois random generator to generate phase modulation ortho Uortho Lortho I = I − Q command for BPSK and QPSK modulation case. Fig.2 shows ortho ortho ortho the CCDF plot of the 16 MHz bandwidth OFDM signals Qortho = Iortho + Qortho without modulation. The probability for a PAPR of 8 dB or The orthogonality products Iortho and Qortho are then larger is of 0.01%. ﬁnally added to the outputs Iinter and Qinter of the interband predistortion block to cancel the unwanted interferences: B. Orthogonality Implementation I = I + I In Ref. [3] two costly Hilbert transforms were used for the out ortho inter frequency selective ﬁltering. In this work, look up table (LUT) Qout = Qortho + Qinter

1078 Orthogonality Implementation α I’ USB Uortho Uortho E’U Orthogonality Coefficients Q’ βUortho Uortho α I’ Inband USB LSB Lortho Lortho E’ Orthogonality Coefficients L Coefficients β Q’ α β Lortho Lortho E U U U

IU I’ Iortho Qortho OFDM U QU I’ I I Generator Q’U in inter out DAC RF (64 Tones) PA IL DAC I’L Q Q Q’ inter Qout L in α β Q’L inter inter α β E L L L LO Interband Inband LSB Coefficients Coefficients

Fig. 3. Fully orthogonal baseband vector predistortion implementation for two bands

III. FPGA IMPLEMENTATION were introduced in the FPGA test-bed to directly control from a Matlab GUI, the DC offset (LO leakage rejection) and the

Fully Orthogonal Vector Predistortion Linearization DAC5682z EVM gain and phase correction required to compensate for the IQ

OFDM Generator I imbalance of the IQ modulator. The methodology used for the Ortho HSMC Connector Adder\Multiplexer out DAC IQ Balancing IQ balancing has been reported in [4]. The power ampliﬁer Limiter Limiter Inband

0 Interband to be linearized is a Freescale LDMOS MRF7S38010HR3. It LO 90 2 Q out provides 15 dB gain and 2 W output at 3.5 GHz. Two other DAC amplifiers are cascaded before the final stage to provide linear FPGA/DSP BB LPF IQ Modulator amplification. 30 dB pre−PA Attenuator PC ULLY RTHOGONAL PREDISTORTION LINEARIZATION PA pre−PA IV. F O Control Spectrum Analyzer RESULTS: The performance of the proposed fully orthogonal predis- Fig. 4. Digital test-bed for fully orthogonal baseband vector tortion linearization algorithm was investigated using OFDM predistortion signals generated from the OFDM signal generator implemented in the FPGA board. IQ balancing of 45 dBc at the The overall experimental test-bed used in this work is de- fundamental inband frequencies was achieved. By controlling scribed in Fig.4. The fully orthogonal linearization algorithm the DC offset, an LO leakage of -50 dBc was obtained. Fig.1 was implemented in a FPGA. This digital test-bed is based on shows the outputs of the up-converted predistortion signals an Altera DSP board (DE3) with the Stratix III 3SL 150. The before passing into PAs, with Fig.1 (a) presenting the interband digital data from DE3 are sent to a TI DAC5682z evaluation predistortion products, and Fig.1 (b) presenting the impact board (EVM) via one of the four HSMC connector banks. The of interband predistortion on inband spectrum regrowth with EVM contains two 16 bits D/A converters (up to 1 GSPS), a and without orthogonality implementation. Clearly with the CDCM7005 clock distribution device and a TRF3703 analog orthogonality implementation, the inband interferences and the quadrature modulator to upconvert the DAC outputs to RF. The resulting inband spectral regrowth caused by the interband DE3 system clock (100 MHz) is distributed via synchronized predistortion are highly suppressed. and delayed clocks to the 16 bit D/A converters. The gain of Fig.5 shows the fully orthogonality linearization of a two- the DACs is scaled in 16 equal steps to increase the current carrier OFDM signal for the LDMOS PA. The vertical scale level of the signals, and the DC offset control is provided by is 5 dB per division and the horizontal scale is 10 MHz per the GUI of the EVM to manually adjust the LO leakage in the division for a total span of 100 MHz. Each OFDM band has a IQ modulator. The LC low-pass filter (LPF) with 300 MHz 3 8 MHz bandwidth. The center of each band is separated by 24 dB corner frequency is positioned between the D/A converters MHz. As shown in Fig.5 (a), the linearization is firstly carried and the modulator. Interpolation filter with ×4 rate together out for the inband, then the interband. Without orthogonality, with the LPF are used to remove the Nyquist images of the the interband predistortion-linearization degrades the already baseband signal. In addition to the manual DC offset and gain linearized inband spectrum by 5 dB. In order to achieve controls implemented in the EVM, several software blocks optimal inband linearization results in the original work [3],

1079 −20 −20 a −25 −25 b Non−linearized Spectrum Non−linearized Spectrum −30 LSB in&inter band linearization without ortho −30 USB in&inter band linearization without ortho LSB in&inter band linearization with ortho USB in&inter band linearization with ortho −35 −35

−40 −40

−45 −45

−50 −50 15dB 15dB

Spectrum (dBm) −55 Spectrum (dBm) −55

−60 −60 5dB 5dB −65 −65

−70 −70

−75 −75 3.45 3.46 3.47 3.48 3.49 3.5 3.51 3.52 3.53 3.54 3.55 3.45 3.46 3.47 3.48 3.49 3.5 3.51 3.52 3.53 3.54 3.55 Frequency (GHz) Frequency (GHz)

−20 demonstrated that with the new orthogonality implementation, the inband distortion introduced by the interband predistortion −25 c Non−linearized Spectrum 8 MHz steps was automatically suppressed such that multiple iterative −30 Linearization without Ortho Linearization with Ortho steps between the two interband and two inband linearizations −35 24 MHz 45dB were no longer required in the optimization. Independent −40 control of the lower and upper side band spectral regrowth was −45 also demonstrated for two-carrier OFDM signal for an overall −50 -45 dBc of ACPR, with 15 dB linearization improvement

Spectrum (dBm) −55 achieved for both inband and interband. This work can be −60 extended from two-carrier to multi-carrier power ampliﬁers

−65 by further dividing the bandwidth in additional bands [5]

−70 and applying the present inband and interband algorithms to

−75 individual band and pairs of bands respectively. This orthog- 3.45 3.46 3.47 3.48 3.49 3.5 3.51 3.52 3.53 3.54 3.55 Frequency (GHz) onal implementation will facilitate the auto-adaptation of the linearization algorithm and will operate with a receiver with Fig. 5. Four-band fully orthogonal frequency selective (a) LSB reduced bandwidth owing to its frequency selective nature. inband and interband, (b) USB inband and interband, (c) joint inband ACKNOWLEDGEMENT and interband LSB and USB predistortion-linearization of a two- carrier OFDM signal for a PA with differential memory This work was supported in part by the National Science Foundation (NSF) under a GOALI grant ECS-0622003 and IUCRC grant IIP-0631286 and a grant from Samsung Corpora- iterative inband and interband linearization steps were needed. tion. We would like to thanks Altera Corporation for donating In contrast, with the novel orthogonality implementation, the the DE3 FPGA testbed. interband predistortion is effectively orthogonal to the inband, resulting in an highly efficient linearization procedure. From REFERENCES Fig.5 (a) and (b), it is verified that the new proposed al- [1] R. Sperlich, J.A. Sills and J. S. Kenney, “Closed-loop Pigital Pre- distortion with Memory Effects Using Digital Pre-distortion and Genetic gorithm could linearize either the upper side or lower side Algorithms,” IEEE MTT Symposium Digest, pp. 1557-1560, June 2005. inband and interband independently justifying the claim of [2] N. Safari, J. P. Tanem and T. Roste, “A Block-Based Predistortion for frequency-selectivity. Fig.5 (c) shows the combined reduction High-Power Amplifier Linearization,” IEEE Transactions on Microwave Theory and Techniques, Vol. 54, No. 6, pp. 2813-2820, June 2006. of the inband and interband spectral regrowth on both sides [3] Roblin P, Sukkeun Myoung, Chaillot D, Young Gi Kim, Fathimulla A, of the LO. The overall performance of the fully orthogonal Strahler J and Bibyk S, “Frequency Selective Predistortion Linearization implementation predistortion linearization for a two-carrier of RF Power Amplifiers,” IEEE Transactions on Microwave Theory and Techniques, Vol. 56, Issue.1, page:65-76, Jan 2008. OFDM signal is of -45 dBc ACPR with 15 dB linearization [4] S.K. Myoung, X. Cui, P. Roblin, D. Chaillot, F. Verbeyst, M. Vanden improvement achieved for both inband and interband. Bossche, S.J. Doo and W. Dai, “Large Signal Network Analyzer with Trigger for Baseband Modulation Linearization,” 64th ARFTG Confer- V. C ONCLUSION ence Digest, Orland, Florida, Dec 2004. [5] O. Hammi, S. Boumaiza, M. Ja¨ıdane-Sa¨ıdane and F. M. Ghannouchi, In this paper, we proposed a novel fully orthogonal baseband “Digital Subband Filtering Predistorter Architecture for Wireless Trans- vector predistortion linearization algorithm for frequency- mitters,” IEEE Transactions on Microwave Theory and Techniques, Vol. selectively linearizing PAs with differential memory effect. We 53, No. 5, pp. 1643-1652, May 2005.

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